On the half-space theorem for minimal surfaces in Heisenberg space

Half-space Theorem, Embedded Minimal Annuli and Minimal Graphs in the Heisenberg Group

We construct a one-parameter family of properly embedded minimal annuli in the Heisenberg group Nil3 endowed with a left-invariant Riemannian metric. These annuli are not rotationally invariant. This family gives a vertical half-space theorem and proves that each complete minimal graph in Nil3 is entire. Also, the sister surface of an entire minimal graph in Nil3 is an entire constant mean curv...

Sym-Bobenko formula for minimal surfaces in Heisenberg space

We give an immersion formula, the Sym-Bobenko formula, for minimal surfaces in the 3-dimensional Heisenberg space. Such a formula can be used to give a generalized Weierstrass type representation and construct explicit examples of minimal surfaces. Mathematics Subject Classification: Primary 53A10, Secondary 53C42.

Minimal Surfaces in Euclidean Space

Fundamental Steady state Solution for the Transversely Isotropic Half Space

Response of a transversely isotropic 3-D half-space subjected to a surface time-harmonic excitation is presented in analytical form. The derivation of the fundamental solutions expressed in terms of displacements is based on the prefect series of displacement potential functions that have been obtained in the companion paper by the authors. First the governing equations are uncoupled in the cyl...

Minimal translation surfaces in hyperbolic space

In the half-space model of hyperbolic space, that is, R+ = {(x, y, z) ∈ R ; z > 0} with the hyperbolic metric, a translation surface is a surface that writes as z = f(x) + g(y) or y = f(x) + g(z), where f and g are smooth functions. We prove that the only minimal translation surfaces (zero mean curvature in all points) are totally geodesic planes. MSC: 53A10